#### A Math Forum Project

 ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary

Student Version

### Scale n' Bowl IV - posted November 22, 1999

(Try Scale 'n Bowl I, Scale 'n Bowl II, and Scale 'n Bowl III before you begin this problem.)

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Find the correct scaling ratio that will enlarge or reduce the blue ball to fit through the green bowling alley and move the two red pins.

1. For alley 1: Find the correct decimal scaling ratio. Put it into percent and fraction forms.

2. For alley 2: Find the correct percent scaling ratio. Put it into decimal and fraction forms.

3. For alley 3: Find the correct fraction scaling ratio. Put it into decimal and percent forms.

4. Put your solutions in order from largest to smallest.

Bonus: Which of the three scaling ratio forms was hardest to use? Which was easiest to use? Why?

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Students had trouble with the interface on this puzzle. They didn't know which equation to use, or what they were supposed to find. In the end, many did not have enough time to finish. In order to make this puzzle easier for students, the interface would need to be changed. Unfortunately, given ESCOT constraints, we were unable to do so.

Most students were successful at finding the correct scaling ratio. Some had difficulty trying to convert this number into the other two forms, but surprisingly, many were successful.

Again, students either did not see it, or did not have time to finish this problem completely, so most did not get full credit. However, students were getting better at making their thinking explicit.

In general, this puzzle (all four parts) did help students learn how to make their guess-and-check strategies explicit. Many did not have time to finish the problem, or simply did not read all of the question/instructions. The last puzzle had an interface issue, which students had difficulty figuring out.

### Highlighted solutions:

 From: Wil D., age 13Jeanette G., age 13 School: School of the Arts, San Francisco, CA

```Page Equivalences

Alley #1
.5, 50%, 1/2-too small
.8, 80%, 4/5-too big
.6, 60%, 3/5-too small
.7, 70%, 7/10-too small
.75, 75%, 3/4- CORRECT!

Alley #2
50%, .5, 1/2-too small
55%, .55, 11/20-too small
60%, .6, 3/5-CORRECT!

Alley #3
2/1, 2, 200%-too big
1/1, 1, 100%-too small
7/5, 1.4, 140%-too big
6/5, 1.2, 120%-CORRECT!

Solutions

Largest-#3 (120%, 6/5, 1.2)
Next largest-#1 (75%, 3/4, .75)
Smallest-#2 (60%, 3/5, .6)

The easiest scaling ratio to use is percent because it is the most clear to
read and you can instantly see how they compare.

The fractions were hardest because of the x/y form.  It is unclear what the
value of the fraction is.

------------------------------------
```

### 2 students received credit this week.

Wil D., age 13 - School of the Arts, San Francisco, CA
Jeanette G., age 13 - School of the Arts, San Francisco, CA